An Efficient Numerical Method for Forward Kinematics of Parallel Robots

Solving the forward kinematics of parallel robots efficiently is important for real-time applications. However, it remains a difficult problem due to its high nonlinearity. This paper combines artificial neural networks and the Global Newton-Raphson with Monotonic Descent (GNRMD) algorithm to decrease the training sets of neural networks while avoiding divergence problem. Furthermore, simplified Newton iteration is introduced to reduce the duration of solution time. The proposed method is demonstrated taking a Stewart platform as an example and the nonlinear equations are established with the geometrical method. Based on the continuous characteristic of real-time applications, the result of the previous solution cycle is used as the initial value of the current solution cycle. Moreover, a threshold adjusting the effective scope of GNRMD algorithm and simplified Newton iteration is set to balance the efficiency and number of iteration. The performance of the algorithm is verified in the environment of Microsoft Visual Studio 2013 based on the continuous feedback of the Stewart platform. Besides, it is compared with GNRMD algorithm and a higher-order numerical method. The results indicate that the proposed algorithm can improve the efficiency of solving the forward kinematics problem.